A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization of HLM

Abstract

This research paper presents a new Latin hypercube sampling method, aimed at enhancing its performance in quantifying uncertainty and reducing computation time. The new Latin hypercube sampling (LHS) method serves as a tool in reliability-based design optimization (RBDO). The quantification technique is termed LHSMDF (LHS with maximum diversity factor). The quantification techniques, such as Latin hypercube sampling (LHS), optimum Latin hypercube sampling (OLHS), and Latin hypercube sampling with maximum diversity factor (LHSMDF), are tested against mechanical components, including a circular shaft housing, a connecting rod, and a cantilever beam, to evaluate its comparative performance. Subsequently, the new method is employed as the basis of RBDO in the synthesis of a six-bar high-lift mechanism (HLM) example to enhance the reliability of the resulting mechanism compared to Monte Carlo simulation (MCS). The design problem of this mechanism is classified as a motion generation problem, incorporating angle and position of the flap as an objective function. The six-bar linkage is first adapted to be a high-lift mechanism (HLM), which is a symmetrical device of the aircraft. Furthermore, a deterministic design, without consideration of uncertainty, may lead to unacceptable performance during the manufacturing step due to link length tolerances. The techniques are combined with an efficient metaheuristic known as teaching–learning-based optimization with a diversity archive (ATLBO-DA) to identify a reliable HLM. Performance testing of the new LHSMDF reveals that it outperforms the original LHS and OLHS. The HLM problem test results demonstrate that achieving optimum HLM with high reliability necessitates precision without sacrificing accuracy in the manufacturing process. Moreover, it is suggested that the six-bar HLM could emerge as a viable option for developing a new high-lift device in aircraft mechanisms for the future.

Keywords

• uncertainty quantification
• LHS
• six-bar linkage
• motion generation
• metaheuristic
• reliability-based design optimization